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3-1.Vectors
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Two forces ${\vec F_1} = 5\hat i + 10\hat j - 20\hat k$ and ${\vec F_2} = 10\hat i - 5\hat j - 15\hat k$ act on a single point. The angle between ${\vec F_1}$ and ${\vec F_2}$ is nearly ....... $^o$
A
$30$
B
$45$
C
$60$
D
$90$
Solution
(b) $\cos \theta = \frac{{\overrightarrow {{F_1}} .\overrightarrow {{F_2}} }}{{|{F_1}||{F_2}|}}$
$ = \frac{{(5\hat i + 10\hat j – 20\hat k).(10\hat i – 5\hat j – 15\hat k)}}{{\sqrt {25 + 100 + 400} \sqrt {100 + 25 + 225} }}$$ = \frac{{50 – 50 + 300}}{{\sqrt {525} \sqrt {350} }}$
$⇒$ $\cos \theta = \frac{1}{{\sqrt 2 }}$
$\therefore $ $\theta = 45^\circ $
Standard 11
Physics
